We are given the following information:

• $n(A \cup B) = 101$
• $n(B) = 74$
• $n(A \cap B) = 47$

We are asked to find $n(A)$, the number of elements in set $A$.

To solve this, we use the principle of inclusion-exclusion:

$n(A \cup B) = n(A) + n(B) - n(A \cap B)$

Substituting the known values:

$101 = n(A) + 74 - 47$

Simplifying:

$101 = n(A) + 27$

Now, solve for $n(A)$:

$n(A) = 101 - 27$

$n(A) = 74$

So, the number of elements in set $A$ is $\boxed{74}$.

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Would you like further clarification or examples? Here are a few related questions:

1. What is the formula for the union of two sets?
2. How do you interpret the intersection of two sets in a Venn diagram?
3. If $n(A \cup B) = n(A) + n(B)$, what does this imply about $A$ and $B$?
4. Can you calculate $n(A \cap B^c)$, the number of elements in $A$ but not in $B$?
5. How would you calculate $n(A \cup B)$ if you know the cardinalities of $A$ and $B$ but not their intersection?

Tip: The principle of inclusion-exclusion helps avoid double-counting when calculating the union of two sets.